Nonexistence of selfsimilar blowup for the nonlinear Dirac equations in (1+1) dimensions
Abstract
We address a general system of nonlinear Dirac equations in (1+1) dimensions and prove nonexistence of classical selfsimilar blowup solutions in the space of bounded functions. While this argument does not exclude the possibility of finitetime blowup, it still suggests that smooth solutions to the nonlinear Dirac equations in (1+1) dimensions do not develop selfsimilar singularities in a finite time. In the particular case of the cubic Dirac equations, we characterize (unbounded) selfsimilar solutions in the closed analytical form.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 DOI:
 10.48550/arXiv.1810.10365
 arXiv:
 arXiv:1810.10365
 Bibcode:
 2018arXiv181010365H
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 Mathematics  Classical Analysis and ODEs
 EPrint:
 8 pages